This invention relates to safety razors of the kind having a blade unit carried by a handle, the blade unit including an elongate blade with a rectilinear sharpened edge, or a plurality of such blades with parallel edges. The blade unit may be fixedly mounted on the handle with the intention that the entire razor be discarded when the blade edge or edges have become dulled. Alternatively, the blade unit can be detachably connected to the handle to enable replacement of a used blade unit with a fresh blade unit. Replaceable blade units are commonly referred to as cartridges.